15.7 : Relative Motion Analysis - Acceleration

A slider-crank mechanism converts rotational motion from the crank into linear motion of the slider or vice versa. This mechanism consists of three main parts: the crank, the connecting rod, and the slider. The movement of the slider-crank is an example of general plane motion as the fluctuating angle between the crank and the connecting rod. Consider a segment AB where point A is at the end of the slider and point B is on the diametrically opposite end to point A, on a crack. The variance in motion of segment AB can be studied by assigning a stationary reference system at point O and an additional translating frame of reference at point A.

The absolute linear velocity at point B can be depicted as the sum of two vectors: the absolute linear velocity of point A and the relative velocity of point B when seen in relation to point A. When time derivatives are taken into account, the absolute acceleration of point B is obtained. This acceleration is effectively the vector sum of the absolute acceleration of point A and the relative acceleration of point B in relation to point A.

The path of point B's motion, when compared to point A, is circular. Consequently, the relative acceleration of point B is expressed in terms of its normal and tangential components. The movement of point B is a result of three factors - the linear acceleration of point A, the angular acceleration, and the angular acceleration of point B when compared to point A. Therefore, the motion in a slider-crank mechanism is a complex interplay of these factors, making it non-uniform.